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In problem 5, the CM of the plate is now...

In problem `5, the CM` of the plate is now in the following quadrant of `x-y` plane.

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To determine the new position of the center of mass (CM) of a uniform square plate after a piece of irregular shape has been removed and glued to the center, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Initial Setup**: - We have a uniform square plate with a piece (Q) removed from it. The plate originally has its center of mass at its geometric center. 2. **Identify the Effect of Removing Piece Q**: - When a piece is removed from the plate, the mass of the plate decreases, and the center of mass will shift towards the remaining mass. Since piece Q is removed, the remaining part of the plate will be heavier compared to the removed piece. 3. **Consider the Position of Piece Q**: - The piece Q is glued to the center of the plate. This means that the mass of piece Q is now effectively concentrated at the center of the plate. 4. **Determine the Direction of the Shift**: - The center of mass will shift towards the heavier side. Since we have removed piece Q, which is lighter than the remaining part of the plate, the center of mass will shift in the opposite direction of the removed piece. 5. **Identify the Quadrants**: - The square plate is divided into four quadrants: - 1st Quadrant: (+x, +y) - 2nd Quadrant: (-x, +y) - 3rd Quadrant: (-x, -y) - 4th Quadrant: (+x, -y) 6. **Conclusion on the New Position of CM**: - If the original center of mass was in the 1st quadrant, the removal of piece Q and its placement at the center will cause the center of mass to shift towards the 3rd quadrant, which is the opposite of the 1st quadrant. ### Final Answer: The center of mass of the plate will lie in the **3rd quadrant** after the piece Q has been removed and glued to the center. ---
To determine the new position of the center of mass (CM) of a uniform square plate after a piece of irregular shape has been removed and glued to the center, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Initial Setup**: - We have a uniform square plate with a piece (Q) removed from it. The plate originally has its center of mass at its geometric center. 2. **Identify the Effect of Removing Piece Q**: ...
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